Free Access
Issue
ESAIM: COCV
Volume 8, 2002
A tribute to JL Lions
Page(s) 873 - 883
DOI https://doi.org/10.1051/cocv:2002044
Published online 15 August 2002
  1. V.I. Agoshkov and G.I. Marchuk, On solvability and numerical solution of data assimilation problems. Russ. J. Numer. Analys. Math. Modelling 8 (1993) 1-16. [CrossRef] [Google Scholar]
  2. R. Bellman, Dynamic Programming. Princeton Univ. Press, New Jersey (1957). [Google Scholar]
  3. R. Glowinski and J.-L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numerica 1 (1994) 269-378. [CrossRef] [Google Scholar]
  4. I.A. Krylov and F.L. Chernousko, On a successive approximation method for solving optimal control problems. Zh. Vychisl. Mat. Mat. Fiz. 2 (1962) 1132-1139 (in Russian). [Google Scholar]
  5. A.B. Kurzhanskii and A.Yu. Khapalov, An observation theory for distributed-parameter systems. J. Math. Syst. Estimat. Control 1 (1991) 389-440. [Google Scholar]
  6. O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type. Nauka, Moscow (1967) (in Russian). [Google Scholar]
  7. F.X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: Theoretical aspects. Tellus 38A (1986) 97-110. [CrossRef] [Google Scholar]
  8. J.-L. Lions, Contrôle Optimal des Systèmes Gouvernés par des Équations aux Dérivées Partielles. Dunod, Paris (1968). [Google Scholar]
  9. J.-L. Lions and E. Magenes, Problémes aux Limites non Homogènes et Applications. Dunod, Paris (1968). [Google Scholar]
  10. J.-L. Lions, On controllability of distributed system. Proc. Natl. Acad. Sci. USA 94 (1997) 4828-4835. [CrossRef] [Google Scholar]
  11. G.I. Marchuk, V.I. Agoshkov and V.P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. CRC Press Inc., New York (1996). [Google Scholar]
  12. G.I. Marchuk and V.I. Lebedev, Numerical Methods in the Theory of Neutron Transport. Harwood Academic Publishers, New York (1986). [Google Scholar]
  13. G.I. Marchuk and V.V. Penenko, Application of optimization methods to the problem of mathematical simulation of atmospheric processes and environment, in Modelling and Optimization of Complex Systems, Proc. of the IFIP-TC7 Work. Conf. Springer, New York (1978) 240-252. [Google Scholar]
  14. G.I. Marchuk and V.P. Shutyaev, Iteration methods for solving a data assimilation problem. Russ. J. Numer. Anal. Math. Modelling 9 (1994) 265-279. [CrossRef] [Google Scholar]
  15. G. Marchuk, V. Shutyaev and V. Zalesny, Approaches to the solution of data assimilation problems, in Optimal Control and Partial Differential Equations. IOS Press, Amsterdam (2001) 489-497. [Google Scholar]
  16. G.I. Marchuk and V.B. Zalesny, A numerical technique for geophysical data assimilation problem using Pontryagin's principle and splitting-up method. Russ. J. Numer. Anal. Math. Modelling 8 (1993) 311-326. [CrossRef] [Google Scholar]
  17. E.I. Parmuzin and V.P. Shutyaev, Numerical analysis of iterative methods for solving evolution data assimilation problems. Russ. J. Numer. Anal. Math. Modelling 14 (1999) 265-274. [CrossRef] [Google Scholar]
  18. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze and E.F. Mischenko, The Mathematical Theory of Optimal Processes. John Wiley, New York (1962). [Google Scholar]
  19. Y.K. Sasaki, Some basic formalisms in numerical variational analysis. Mon. Wea. Rev. 98 (1970) 857-883. [Google Scholar]
  20. V.P. Shutyaev, On a class of insensitive control problems. Control and Cybernetics 23 (1994) 257-266. [MathSciNet] [Google Scholar]
  21. V.P. Shutyaev, Some properties of the control operator in a data assimilation problem and algorithms for its solution. Differential Equations 31 (1995) 2035-2041. [MathSciNet] [Google Scholar]
  22. V.P. Shutyaev, On data assimilation in a scale of Hilbert spaces. Differential Equations 34 (1998) 383-389. [MathSciNet] [Google Scholar]
  23. A.N. Tikhonov, On the solution of ill-posed problems and the regularization method. Dokl. Akad. Nauk SSSR 151 (1963) 501-504. [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.